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   "source": [
    "## 一元线性回归\n",
    "\n",
    "以一元为例，$y=w_1x_1+b=w^Tb=w_1x_1+w_0x_0$, 实际使用梯度下降法时可以令$x_0=0$,则求出的$w_0=b$\n",
    "\n",
    "### 梯度下降法\n",
    "\n",
    "![jupyter](./BGD.png)"
   ],
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     "text": [
      "输出参数w: [[1.42719063]]\n输出参数:b [0.2380875]\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def true_fun(X):\n",
    "    return 1.5*X + 0.2\n",
    "\n",
    "np.random.seed(0) # 随机种子\n",
    "n_samples = 30\n",
    "'''生成随机数据作为训练集'''\n",
    "train_X = np.sort(np.random.rand(n_samples)) \n",
    "train_y = (true_fun(train_X) + np.random.randn(n_samples) * 0.05).reshape(n_samples,1)\n",
    "data_X = []\n",
    "for x in train_X:\n",
    "    data_X.append([1,x])\n",
    "data_X = np.array((data_X))\n",
    "maxiter = 200 # 迭代数\n",
    "m,n = shape(data_X)\n",
    "weights = ones((n,1))\n",
    "alpha = 0.01 # 学习率\n",
    "for i in range(0,maxiter):\n",
    "    hypothesis = np.dot(data_X,weights)\n",
    "    error = (hypothesis-train_y)\n",
    "    gradient = data_X.transpose().dot(error)\n",
    "    weights = weights - alpha * gradient\n",
    "print(\"输出参数w:\",weights[1:]) # 输出模型参数w\n",
    "print(\"输出参数:b\",weights[0]) # 输出参数b\n",
    "\n",
    "\n",
    "test_X = np.linspace(0, 1, 100)\n",
    "plt.plot(test_X, test_X*weights[1][0]+weights[0][0], label=\"Model\")\n",
    "plt.plot(test_X, true_fun(test_X), label=\"True function\")\n",
    "plt.scatter(train_X,train_y) # 画出训练集的点\n",
    "plt.legend(loc=\"best\")"
   ]
  },
  {
   "source": [
    "## scikit-learn\n",
    "scikit-learn，简称sklearn，是一个开源的基于python语言的机器学习工具包。它通过NumPy, SciPy和Matplotlib等python数值计算的库实现高效的算法应用，并且涵盖了几乎所有主流机器学习算法。\n",
    "\n",
    "官网：https://scikit-learn.org/stable/index.html"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "输出参数w: [1.4474774]\n输出参数:b 0.22557541560416694\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb6a880d650>"
      ]
     },
     "metadata": {},
     "execution_count": 35
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression # 导入线性回归模型\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import learning_curve\n",
    "\n",
    "def true_fun(X):\n",
    "    return 1.5*X + 0.2\n",
    "\n",
    "np.random.seed(0) # 随机种子\n",
    "n_samples = 30\n",
    "'''生成随机数据作为训练集'''\n",
    "train_X = np.sort(np.random.rand(n_samples)) \n",
    "train_y = true_fun(train_X) + np.random.randn(n_samples) * 0.05\n",
    "\n",
    "model = LinearRegression() # 定义模型\n",
    "model.fit(train_X[:,np.newaxis], train_y) # 训练模型\n",
    "\n",
    "print(\"输出参数w:\",model.coef_) # 输出模型参数w\n",
    "print(\"输出参数:b\",model.intercept_) # 输出参数b\n",
    "\n",
    "test_X = np.linspace(0, 1, 100)\n",
    "plt.plot(test_X, model.predict(test_X[:, np.newaxis]), label=\"Model\")\n",
    "plt.plot(test_X, true_fun(test_X), label=\"True function\")\n",
    "plt.scatter(train_X,train_y) # 画出训练集的点\n",
    "plt.legend(loc=\"best\")"
   ]
  },
  {
   "source": [
    "## 多元线性回归\n",
    "\n",
    "以三元为例，$y=w_1x_1+w_2x_2+w_3x_3+b=w^Tb$"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "输出参数w: [[0. 2. 3.]]\n输出参数b: [1.]\n预测结果: [[22.]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "X = [[1,1,1],[1,1,2],[1,2,1]]\n",
    "y = [[6],[9],[8]]\n",
    " \n",
    "model = LinearRegression()\n",
    "model.fit(X, y)\n",
    "print(\"输出参数w:\",model.coef_) # 输出参数w1,w2,w3\n",
    "print(\"输出参数b:\",model.intercept_) # 输出参数b\n",
    "test_X = [[1,3,5]]\n",
    "pred_y = model.predict(test_X)\n",
    "print(\"预测结果:\",pred_y)"
   ]
  },
  {
   "source": [
    "## 多项式回归以及过拟合与欠拟合"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "\n",
    "\n",
    "### 训练集\n",
    "用来训练模型内参数的数据集\n",
    "\n",
    "### 验证集\n",
    "用于在训练过程中检验模型的状态，收敛情况，通常用于调整超参数，根据几组模型验证集上的表现决定哪组超参数拥有最好的性能。\n",
    "\n",
    "同时验证集在训练过程中还可以用来监控模型是否发生过拟合，一般来说验证集表现稳定后，若继续训练，训练集表现还会继续上升，但是验证集会出现不升反降的情况，这样一般就发生了过拟合。所以验证集也用来判断何时停止训练\n",
    "\n",
    "### 测试集\n",
    "测试集用来评价模型泛化能力，即使用训练集调整了参数，之前模型使用验证集确定了超参数，最后使用一个不同的数据集来检查模型。\n",
    "\n",
    "### 交叉验证\n",
    "\n",
    "交叉验证法的作用就是尝试利用不同的训练集/测试集划分来对模型做多组不同的训练/测试，来应对测试结果过于片面以及训练数据不足的问题。\n",
    "\n",
    "![jupyter](./cross_valid.png)\n",
    "\n",
    "\n",
    "\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "def true_fun(X):\n",
    "    return np.cos(1.5 * np.pi * X)\n",
    "np.random.seed(0)\n",
    "\n",
    "n_samples = 30\n",
    "degrees = [1, 4, 15] # 多项式最高次\n",
    "\n",
    "X = np.sort(np.random.rand(n_samples)) \n",
    "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n",
    "\n",
    "plt.figure(figsize=(14, 5))\n",
    "for i in range(len(degrees)):\n",
    "    ax = plt.subplot(1, len(degrees), i + 1)\n",
    "    plt.setp(ax, xticks=(), yticks=())\n",
    "\n",
    "    polynomial_features = PolynomialFeatures(degree=degrees[i],\n",
    "                                             include_bias=False)\n",
    "    linear_regression = LinearRegression()\n",
    "    pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n",
    "                         (\"linear_regression\", linear_regression)]) # 使用pipline串联模型\n",
    "    pipeline.fit(X[:, np.newaxis], y)\n",
    "\n",
    "    # 使用交叉验证\n",
    "    scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n",
    "                             scoring=\"neg_mean_squared_error\", cv=10)\n",
    "\n",
    "    X_test = np.linspace(0, 1, 100)\n",
    "    plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
    "    plt.plot(X_test, true_fun(X_test), label=\"True function\")\n",
    "    plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.xlim((0, 1))\n",
    "    plt.ylim((-2, 2))\n",
    "    plt.legend(loc=\"best\")\n",
    "    plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n",
    "        degrees[i], -scores.mean(), scores.std()))\n",
    "plt.show()"
   ]
  }
 ]
}